Chapter 10 - CHAPTER 10 ARBITRAGE PRICING THEORY AND...

• Notes
• 12
• 100% (1) 1 out of 1 people found this document helpful

This preview shows pages 1–3. Sign up to view the full content.

CHAPTER 10 ARBITRAGE PRICING THEORY AND MULTIFACTOR MODLES OF RISK AND RETURN 10.1 MULTIFACTOR MODELS: AN OVERVIEW 1. Multifactor Models of Security Returns The index model introduced earlier in this handout give us a way of decomposing stock variability into market or systematic versus firm-specific effects that can be diversified in large portfolios. In the index model, the return on the market portfolio summarizes the aggregate impact of macro factors. In reality, however, systematic risk is not due to one source, but instead derives from uncertainty in many economy-wide factors such as business-cycle risk, interest or inflation rate risk, energy price risk, etc. How can we improve on the single-index model but still maintain the useful dichotomy between systematic and diversifiable risk? It is easy to see that models that allow for several systematic factors – multifactor models – can provide better description of security returns. Let’s illustrate with a two-factor model. Suppose the two most important macroeconomic sources of risk are uncertainties surrounding the state of the business cycle, news of which we again assume is reflected in the rate of return on a broad index such as the S&P 500, and unanticipated changes in interest rates, which may be captured by the return on a T-bond portfolio. The return on any stock will respond to both sources of macro risk as well as to its own firm-specific influences. Therefore, we can generalize the single-index model into a two-factor model describing the excess rate of return on a stock i in some time period t as follows: it TBt iTB Mt iM i it e R β R β α R , (1) where TB is the sensitivity of the stock’ excess return to that of the T-bond portfolio, and R TB is the excess return of the T-bill portfolio in month t . The two indexes on the right-hand side of the equation capture the effect of the two systematic factors in the economy; thus they play the role of the market index in the single-index model. As before, e t reflects firm-specific influences in period t . How will the security market line of the CAPM generalize once we recognize the presence of multiple sources of systematic risk? Perhaps, not surprisingly, a multifactor index model gives rise to a multifactor security market line (SML) in which the risk premium is determined by the exposure to each systematic risk 1

This preview has intentionally blurred sections. Sign up to view the full version.

factor and by a risk premium associated with each of those factors. Such a multifactor CAPM was first presented by Merton (1973). For example, in a two- factor economy in which the risk exposure can be measure by the equation (1), the expected rate of return on a security i would be express as follows: ] r ) [E(r β ] r ) [E(r β r ) E(r f TB iTB f M iM f i (2) It is clear that the equation above is a generalization of the simple security market line. In the single-factor SML, the benchmark risk premium is given by the risk premium of the market portfolio, but once we generalize to multiple risk
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern